“….Perez III In the same spirit when ω is not open, we have shown in the paper[10, Lemma 4.5] that if f, g ∈ H 2 (D) and|f (z)| = |g(z)|, z ∈ (−1, 1) ∪ e iα (−1, 1)where α / ∈ πQ, then f and g are equal up to the multiplication of a unimodular constant. For this result, uniqueness was established by showing that the Blaschke products, singular inner parts, and outer parts of f and g are equal.…”